Digital wireless communications are being widely used throughout the world particularly with the latest development of the Orthogonal Frequency Division Multiplex (OFDM systems) and the latest evolution, namely the so-called Long Term Evolution (LTE), DVB-H, WiFi 802.11 and WiMax 802.16 systems.
OFDM is a frequency-division multiplexing (OFDM) scheme utilized as a digital multi-carrier modulation method. As it is well known to one skilled in the art, OFDM systems demonstrate significant advantages in comparison to single-carrier schemes, particularly in their ability to cope with severe channel conditions (i.e., channel attenuation, narrowband interference, frequency-selective fading).
The combination of OFDM and multiple antennas in either the transmitter or receiver is attractive to increase a diversity gain.
In that respect, the well known ALAMOUTI scheme, as disclosed in document “A simple transmit diversity technique for wireless communications”, by in S. M. ALAMOUTI, IEEE J. Selected Areas of Communications, vol. 16, pp. 1451-1458, October 1998, has revealed to be extremely efficient in allowing wireless and cellular systems to increase link reliability. Its efficiency proves because of the extremely simple encoding technique at the transmitter and more importantly in the low complexity linear and optimal decoding which can also easily be extended to multiple receiving antenna case.
With respect to FIG. 1, there is recalled the general principle of the transmission scheme in accordance with the ALAMOUTI Space Time Block coding.
Considering, as shown in the figure that the following sequence of complex symbols should be transmitted: x1, x2, x3, x4.
In normal transmission, a first time slot would be allocated for the transmission of x1, a second time slot would be allocated for x2 etc.
Now, considering the ALAMOUTI scheme and more particularly the Space-Time Block Code (STBC), those symbols are now grouped in two.
During the first time slot, x1 and x2 are respectively transmitted by the first and second antenna while, in the second time slot, −x2* and x1* are respectively sent through the first and second antenna. In the third time slot, x3 and x4 are transmitted by the first and second antenna while, in the fourth time slot, the two antennas transmit −x4* and x3*, respectively, and so on.
It can be noticed that such block coding has no effect on the data rate since two time slots are still required for the transmission of two symbols.
In the first time slot, the receiver receives the signal:y1=h1x1+h2x2+n1 
In the second time slot, the received signal is,y2=−h1x*2+h2x*1+n2 where
y1, y2 is the received symbol on the first and second time slot respectively,
h1 is the channel from 1st transmit antenna to receive antenna,
h2 is the channel from 2nd transmit antenna to receive antenna,
x1, x2 are the transmitted symbols and
n1 n2, is the noise on 1st and 2nd time slots.
What can be expressed as follows:
                              [                                                                      y                  1                                                                                                      y                  2                  *                                                              ]                =                                            [                                                                                          h                      1                                                                                                  h                      2                                                                                                                                                          h                        ~                                            2                      *                                                                                                  -                                                                        h                          ~                                                1                        *                                                                                                        ]                        ⁡                          [                                                                                          x                      1                                                                                                                                  x                      2                                                                                  ]                                +                      [                                                                                n                    1                                                                                                                    n                    2                    *                                                                        ]                                              (        1        )            
Let us define
  H  =            [                                                  h              1                                                          h              2                                                                          h              2              *                                                          -                              h                1                *                                                        ]        .  And H+ being the pseudo inverse defined as: H+=(HH H)−1HH 
Solving the equation Y=Ax above, leads to the following
                                          [                                                                                x                    1                                                                                                                    x                    2                    *                                                                        ]                    ^                =                                            (                                                H                  H                                ⁢                H                            )                                      -              1                                ⁢                                    H              H                        ⁡                          [                                                                                          y                      1                                                                                                                                  y                      2                      *                                                                                  ]                                                          (        2        )            
Applied to the frequency domain rather than in the time domain, the ALAMOUTI block coding results, in the so-called Space-Frequency Block Code (SFBC), two consecutive and neighboring subcarriers within the same OFDM symbol, instead of two consecutive time slots.
The use of such space block significantly increases the link reliability of wireless and cellular systems without requiring a significant increase in the complexity of the receiver.
It is particularly effective because of the extremely simple encoding technique at the transmitter and more importantly in the low complexity linear and optimal decoding which can also easily be extended to multiple receiving antenna case.
However, such benefit strongly relies on the assumption that the channel remains constant over two time slots or, in OFDM, between two neighboring subcarriers or resources.
Such assumption of static conditions over the two periods or channel uses spanning its transmission is actually never verified in practice and remains ideal.
In OFDM, the channel is selective because of the time-varying or frequency selective nature of the terminal mobility and the rich scattering of the wireless environment:
long channel delay spread, e.g., hilly terrain propagation
low channel coherence bandwidth, i.e., high relative speed between the base station (BS) and the wireless mobile receiver.
When the static assumption is not verified, the demodulation process tends to become much more complicated.
Indeed, the conventional low complexity methods, such as the very basic matched filter, and even the more sophisticated linear processings (Zero-forcing, MMSE equalization) shows little efficiency and remain sub-optimal.
The well known Maximum Likelihood would be optimal but becomes highly complex as the size of the modulation increases (exponential complexity of the order of 2M), where M is the order of the modulation used, i.e., M=2 for QPSK, M=4 for 16-QAM and M=6 for 64-QAM.
On the other hand, the Near-ML detection based on Sphere Decoding: optimal (slight decrease in coding gain) could be another solution, but still shows high level of complexity (polynomial complexity in function of modulation order M3 in average).
Therefore, there is a desire for a new method which allows decoding of the ALAMUTI code, with low complexity, even in the case where the channel shows variation between two neighboring subcarriers or OFDM blocks.